If 2000 electric field lines enter a given volume of closed space and 4000 field lines diverge from it, then the total charge within the volume is (Given \( \epsilon_0 = 8.85 \times 10^{-12} \text{ C}^2\text{m}^{-2}\text{N} \))

A straight wire of mass 200 g and length 1.5 m carries a current of 2 A. It is suspended in mid air by a uniform horizontal magnetic field B perpendicular to length of wire. The magnitude of B is ( \( g = 10 \text{ ms}^{-2} \) )

In a hydrogen atom, an electron moves in an orbit of radius \( 5 \times 10^{-11} \text{ m} \) with a speed of \( 2.2 \times 10^6 \text{ m/s} \). The equivalent current is

From the following, choose the element for impurity atoms with which pure silicon should be doped to make it a p-type semiconductor:

The wavelength of second line of Balmer series in terms of Rydberg constant R is

A battery with potential V across it is connected to a combination of two identical resistors, and then has current i through it. What are the potential difference across and the current through either resistor if the resistors are connected in series ?

Three charges, each equal to +q, are placed at the corners of an equilateral triangle ABC of side 'a' as shown in the figure. P and R are the mid-points of BC and CA. The work done in taking a charge Q from point P to R is:

Read the passage carefully and answer the questions
The carbonyl group of aldehydes and ketones is highly polar. The positively charged carbon is readily attacked by electron-rich nucleophile and the negatively charged oxygen atom is attacked by an electro-deficient electrophile. Aldehydes and ketones undergo nucleophilic addition reactions in the presence of acid or a base. The mechanism involves attack of a nucleophile on the electron deficient carbonyl carbon to form a tetrahedral intermediate. A new bond is formed between the carbon and oxygen. Protonation of the anion furnished by the reaction medium yields a neutral addition product. The addition product is same whether the reaction is catalyzed by acid or a base. For example in the presence of base aldehydes and ketones react with hydrogen cyanide to form cyanohydrin.
The source of nucleophile in the base catalyzed cyanohydrin formation is:

In a series LCR circuit an ac voltage source is connected. When inductor is removed from the circuit, the phase difference between the voltage and the current in the circuit is \( \frac{\pi}{3} \). If capacitor is removed from the circuit instead of inductor, the phase difference is again \( \frac{\pi}{3} \). What is the power factor of the circuit?

Let \(*\) be a binary operation on set \(Q\) of rational numbers given by \(a * b=a+b+a b\).
Then identity element is:

The mathematical expression that represents the Exponential growth in a population is:

Which of the following is the correct expression of the "central dogma" ?

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is four. The probability that it is actually four is :